Isolated singular points and the Gauss-Manin connection

This thesis studies the Gauss-Manin connection for the Milnor fibration of a complex hypersurface with an isolated singular point. Using the formalism developed by Brieskorn and Malgrange, we give an explicit basis, with respect to which the connection has a simple pole and its residue matrix has a manageable form. We calculate the residue for several examples. The method of calculation enables us to give some examples relevant to questions arising in Malgrange's work on the Bernstein polynomial. We also make several conjectures related to the monodromy theorem.